Properties

Label 60.3.c.a.31.5
Level $60$
Weight $3$
Character 60.31
Analytic conductor $1.635$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 60.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.63488158616\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.85100625.1
Defining polynomial: \(x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} + 2 x^{3} - 8 x^{2} - 8 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 31.5
Root \(-0.600040 - 1.28061i\) of defining polynomial
Character \(\chi\) \(=\) 60.31
Dual form 60.3.c.a.31.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.67986 - 1.08539i) q^{2} +1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +2.23607 q^{5} +(1.87994 + 2.90961i) q^{6} +0.596540i q^{7} +(-1.19648 - 7.91002i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(1.67986 - 1.08539i) q^{2} +1.73205i q^{3} +(1.64388 - 3.64660i) q^{4} +2.23607 q^{5} +(1.87994 + 2.90961i) q^{6} +0.596540i q^{7} +(-1.19648 - 7.91002i) q^{8} -3.00000 q^{9} +(3.75629 - 2.42700i) q^{10} +9.27963i q^{11} +(6.31609 + 2.84728i) q^{12} -23.5117 q^{13} +(0.647476 + 1.00210i) q^{14} +3.87298i q^{15} +(-10.5953 - 11.9891i) q^{16} +3.97751 q^{17} +(-5.03959 + 3.25616i) q^{18} -7.04756i q^{19} +(3.67582 - 8.15404i) q^{20} -1.03324 q^{21} +(10.0720 + 15.5885i) q^{22} +32.0793i q^{23} +(13.7006 - 2.07237i) q^{24} +5.00000 q^{25} +(-39.4964 + 25.5192i) q^{26} -5.19615i q^{27} +(2.17534 + 0.980637i) q^{28} +35.6734 q^{29} +(4.20368 + 6.50608i) q^{30} -59.2585i q^{31} +(-30.8115 - 8.64000i) q^{32} -16.0728 q^{33} +(6.68167 - 4.31713i) q^{34} +1.33390i q^{35} +(-4.93163 + 10.9398i) q^{36} -5.38761 q^{37} +(-7.64932 - 11.8389i) q^{38} -40.7234i q^{39} +(-2.67541 - 17.6873i) q^{40} +40.0791 q^{41} +(-1.73570 + 1.12146i) q^{42} +36.1157i q^{43} +(33.8391 + 15.2545i) q^{44} -6.70820 q^{45} +(34.8184 + 53.8888i) q^{46} -74.0131i q^{47} +(20.7657 - 18.3517i) q^{48} +48.6441 q^{49} +(8.39931 - 5.42693i) q^{50} +6.88925i q^{51} +(-38.6503 + 85.7376i) q^{52} -2.55123 q^{53} +(-5.63983 - 8.72882i) q^{54} +20.7499i q^{55} +(4.71864 - 0.713748i) q^{56} +12.2067 q^{57} +(59.9265 - 38.7194i) q^{58} +36.4026i q^{59} +(14.1232 + 6.36670i) q^{60} -8.73223 q^{61} +(-64.3183 - 99.5461i) q^{62} -1.78962i q^{63} +(-61.1369 + 18.9284i) q^{64} -52.5737 q^{65} +(-27.0001 + 17.4452i) q^{66} +69.7379i q^{67} +(6.53853 - 14.5044i) q^{68} -55.5630 q^{69} +(1.44780 + 2.24077i) q^{70} -59.2170i q^{71} +(3.58944 + 23.7301i) q^{72} -83.0019 q^{73} +(-9.05044 + 5.84763i) q^{74} +8.66025i q^{75} +(-25.6996 - 11.5853i) q^{76} -5.53566 q^{77} +(-44.2006 - 68.4098i) q^{78} +65.8705i q^{79} +(-23.6919 - 26.8085i) q^{80} +9.00000 q^{81} +(67.3274 - 43.5013i) q^{82} +129.909i q^{83} +(-1.69851 + 3.76780i) q^{84} +8.89398 q^{85} +(39.1995 + 60.6695i) q^{86} +61.7882i q^{87} +(73.4020 - 11.1029i) q^{88} -130.466 q^{89} +(-11.2689 + 7.28099i) q^{90} -14.0256i q^{91} +(116.980 + 52.7344i) q^{92} +102.639 q^{93} +(-80.3327 - 124.332i) q^{94} -15.7588i q^{95} +(14.9649 - 53.3671i) q^{96} +93.1113 q^{97} +(81.7155 - 52.7977i) q^{98} -27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} + 10q^{4} - 6q^{6} - 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q + 4q^{2} + 10q^{4} - 6q^{6} - 20q^{8} - 24q^{9} + 10q^{10} + 16q^{13} - 20q^{14} + 34q^{16} - 12q^{18} - 40q^{20} - 48q^{21} + 68q^{22} + 18q^{24} + 40q^{25} - 36q^{26} + 28q^{28} + 64q^{29} - 76q^{32} - 92q^{34} - 30q^{36} - 112q^{37} - 40q^{38} - 10q^{40} - 16q^{41} + 108q^{42} + 172q^{44} + 152q^{46} + 48q^{48} - 56q^{49} + 20q^{50} - 128q^{52} + 352q^{53} + 18q^{54} + 116q^{56} + 144q^{57} - 204q^{58} + 30q^{60} - 176q^{61} - 56q^{62} - 110q^{64} - 80q^{65} + 108q^{66} - 184q^{68} - 96q^{69} - 60q^{70} + 60q^{72} - 240q^{73} + 132q^{74} - 24q^{76} - 288q^{77} - 240q^{78} - 80q^{80} + 72q^{81} + 40q^{82} - 36q^{84} + 160q^{85} - 200q^{86} + 140q^{88} + 80q^{89} - 30q^{90} + 144q^{92} + 144q^{93} - 96q^{94} - 174q^{96} + 432q^{97} + 660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67986 1.08539i 0.839931 0.542693i
\(3\) 1.73205i 0.577350i
\(4\) 1.64388 3.64660i 0.410969 0.911649i
\(5\) 2.23607 0.447214
\(6\) 1.87994 + 2.90961i 0.313324 + 0.484935i
\(7\) 0.596540i 0.0852199i 0.999092 + 0.0426100i \(0.0135673\pi\)
−0.999092 + 0.0426100i \(0.986433\pi\)
\(8\) −1.19648 7.91002i −0.149560 0.988753i
\(9\) −3.00000 −0.333333
\(10\) 3.75629 2.42700i 0.375629 0.242700i
\(11\) 9.27963i 0.843602i 0.906688 + 0.421801i \(0.138602\pi\)
−0.906688 + 0.421801i \(0.861398\pi\)
\(12\) 6.31609 + 2.84728i 0.526341 + 0.237273i
\(13\) −23.5117 −1.80859 −0.904295 0.426907i \(-0.859603\pi\)
−0.904295 + 0.426907i \(0.859603\pi\)
\(14\) 0.647476 + 1.00210i 0.0462483 + 0.0715789i
\(15\) 3.87298i 0.258199i
\(16\) −10.5953 11.9891i −0.662209 0.749319i
\(17\) 3.97751 0.233971 0.116986 0.993134i \(-0.462677\pi\)
0.116986 + 0.993134i \(0.462677\pi\)
\(18\) −5.03959 + 3.25616i −0.279977 + 0.180898i
\(19\) 7.04756i 0.370924i −0.982651 0.185462i \(-0.940622\pi\)
0.982651 0.185462i \(-0.0593782\pi\)
\(20\) 3.67582 8.15404i 0.183791 0.407702i
\(21\) −1.03324 −0.0492018
\(22\) 10.0720 + 15.5885i 0.457817 + 0.708568i
\(23\) 32.0793i 1.39475i 0.716705 + 0.697376i \(0.245649\pi\)
−0.716705 + 0.697376i \(0.754351\pi\)
\(24\) 13.7006 2.07237i 0.570857 0.0863486i
\(25\) 5.00000 0.200000
\(26\) −39.4964 + 25.5192i −1.51909 + 0.981509i
\(27\) 5.19615i 0.192450i
\(28\) 2.17534 + 0.980637i 0.0776907 + 0.0350227i
\(29\) 35.6734 1.23012 0.615059 0.788481i \(-0.289132\pi\)
0.615059 + 0.788481i \(0.289132\pi\)
\(30\) 4.20368 + 6.50608i 0.140123 + 0.216869i
\(31\) 59.2585i 1.91156i −0.294076 0.955782i \(-0.595012\pi\)
0.294076 0.955782i \(-0.404988\pi\)
\(32\) −30.8115 8.64000i −0.962860 0.270000i
\(33\) −16.0728 −0.487054
\(34\) 6.68167 4.31713i 0.196520 0.126974i
\(35\) 1.33390i 0.0381115i
\(36\) −4.93163 + 10.9398i −0.136990 + 0.303883i
\(37\) −5.38761 −0.145611 −0.0728055 0.997346i \(-0.523195\pi\)
−0.0728055 + 0.997346i \(0.523195\pi\)
\(38\) −7.64932 11.8389i −0.201298 0.311551i
\(39\) 40.7234i 1.04419i
\(40\) −2.67541 17.6873i −0.0668853 0.442184i
\(41\) 40.0791 0.977539 0.488769 0.872413i \(-0.337446\pi\)
0.488769 + 0.872413i \(0.337446\pi\)
\(42\) −1.73570 + 1.12146i −0.0413261 + 0.0267014i
\(43\) 36.1157i 0.839901i 0.907547 + 0.419950i \(0.137953\pi\)
−0.907547 + 0.419950i \(0.862047\pi\)
\(44\) 33.8391 + 15.2545i 0.769070 + 0.346694i
\(45\) −6.70820 −0.149071
\(46\) 34.8184 + 53.8888i 0.756922 + 1.17150i
\(47\) 74.0131i 1.57475i −0.616477 0.787373i \(-0.711441\pi\)
0.616477 0.787373i \(-0.288559\pi\)
\(48\) 20.7657 18.3517i 0.432620 0.382327i
\(49\) 48.6441 0.992738
\(50\) 8.39931 5.42693i 0.167986 0.108539i
\(51\) 6.88925i 0.135083i
\(52\) −38.6503 + 85.7376i −0.743275 + 1.64880i
\(53\) −2.55123 −0.0481364 −0.0240682 0.999710i \(-0.507662\pi\)
−0.0240682 + 0.999710i \(0.507662\pi\)
\(54\) −5.63983 8.72882i −0.104441 0.161645i
\(55\) 20.7499i 0.377270i
\(56\) 4.71864 0.713748i 0.0842614 0.0127455i
\(57\) 12.2067 0.214153
\(58\) 59.9265 38.7194i 1.03321 0.667576i
\(59\) 36.4026i 0.616993i 0.951225 + 0.308497i \(0.0998259\pi\)
−0.951225 + 0.308497i \(0.900174\pi\)
\(60\) 14.1232 + 6.36670i 0.235387 + 0.106112i
\(61\) −8.73223 −0.143151 −0.0715757 0.997435i \(-0.522803\pi\)
−0.0715757 + 0.997435i \(0.522803\pi\)
\(62\) −64.3183 99.5461i −1.03739 1.60558i
\(63\) 1.78962i 0.0284066i
\(64\) −61.1369 + 18.9284i −0.955264 + 0.295756i
\(65\) −52.5737 −0.808826
\(66\) −27.0001 + 17.4452i −0.409092 + 0.264321i
\(67\) 69.7379i 1.04086i 0.853903 + 0.520432i \(0.174229\pi\)
−0.853903 + 0.520432i \(0.825771\pi\)
\(68\) 6.53853 14.5044i 0.0961548 0.213300i
\(69\) −55.5630 −0.805261
\(70\) 1.44780 + 2.24077i 0.0206828 + 0.0320110i
\(71\) 59.2170i 0.834043i −0.908897 0.417021i \(-0.863074\pi\)
0.908897 0.417021i \(-0.136926\pi\)
\(72\) 3.58944 + 23.7301i 0.0498534 + 0.329584i
\(73\) −83.0019 −1.13701 −0.568506 0.822679i \(-0.692478\pi\)
−0.568506 + 0.822679i \(0.692478\pi\)
\(74\) −9.05044 + 5.84763i −0.122303 + 0.0790220i
\(75\) 8.66025i 0.115470i
\(76\) −25.6996 11.5853i −0.338153 0.152438i
\(77\) −5.53566 −0.0718917
\(78\) −44.2006 68.4098i −0.566675 0.877048i
\(79\) 65.8705i 0.833804i 0.908951 + 0.416902i \(0.136884\pi\)
−0.908951 + 0.416902i \(0.863116\pi\)
\(80\) −23.6919 26.8085i −0.296149 0.335106i
\(81\) 9.00000 0.111111
\(82\) 67.3274 43.5013i 0.821065 0.530503i
\(83\) 129.909i 1.56517i 0.622542 + 0.782586i \(0.286100\pi\)
−0.622542 + 0.782586i \(0.713900\pi\)
\(84\) −1.69851 + 3.76780i −0.0202204 + 0.0448547i
\(85\) 8.89398 0.104635
\(86\) 39.1995 + 60.6695i 0.455808 + 0.705459i
\(87\) 61.7882i 0.710209i
\(88\) 73.4020 11.1029i 0.834114 0.126169i
\(89\) −130.466 −1.46591 −0.732956 0.680277i \(-0.761860\pi\)
−0.732956 + 0.680277i \(0.761860\pi\)
\(90\) −11.2689 + 7.28099i −0.125210 + 0.0808999i
\(91\) 14.0256i 0.154128i
\(92\) 116.980 + 52.7344i 1.27152 + 0.573200i
\(93\) 102.639 1.10364
\(94\) −80.3327 124.332i −0.854603 1.32268i
\(95\) 15.7588i 0.165882i
\(96\) 14.9649 53.3671i 0.155885 0.555908i
\(97\) 93.1113 0.959911 0.479955 0.877293i \(-0.340653\pi\)
0.479955 + 0.877293i \(0.340653\pi\)
\(98\) 81.7155 52.7977i 0.833831 0.538752i
\(99\) 27.8389i 0.281201i
\(100\) 8.21938 18.2330i 0.0821938 0.182330i
\(101\) −3.66081 −0.0362457 −0.0181228 0.999836i \(-0.505769\pi\)
−0.0181228 + 0.999836i \(0.505769\pi\)
\(102\) 7.47749 + 11.5730i 0.0733087 + 0.113461i
\(103\) 151.417i 1.47007i −0.678032 0.735033i \(-0.737167\pi\)
0.678032 0.735033i \(-0.262833\pi\)
\(104\) 28.1313 + 185.978i 0.270493 + 1.78825i
\(105\) −2.31039 −0.0220037
\(106\) −4.28571 + 2.76907i −0.0404313 + 0.0261233i
\(107\) 82.8092i 0.773918i −0.922097 0.386959i \(-0.873526\pi\)
0.922097 0.386959i \(-0.126474\pi\)
\(108\) −18.9483 8.54183i −0.175447 0.0790910i
\(109\) −7.36835 −0.0675996 −0.0337998 0.999429i \(-0.510761\pi\)
−0.0337998 + 0.999429i \(0.510761\pi\)
\(110\) 22.5216 + 34.8569i 0.204742 + 0.316881i
\(111\) 9.33161i 0.0840685i
\(112\) 7.15197 6.32054i 0.0638569 0.0564334i
\(113\) 65.0370 0.575549 0.287774 0.957698i \(-0.407085\pi\)
0.287774 + 0.957698i \(0.407085\pi\)
\(114\) 20.5056 13.2490i 0.179874 0.116219i
\(115\) 71.7315i 0.623752i
\(116\) 58.6427 130.087i 0.505540 1.12144i
\(117\) 70.5350 0.602864
\(118\) 39.5109 + 61.1514i 0.334838 + 0.518232i
\(119\) 2.37274i 0.0199390i
\(120\) 30.6354 4.63395i 0.255295 0.0386163i
\(121\) 34.8885 0.288335
\(122\) −14.6689 + 9.47784i −0.120237 + 0.0776872i
\(123\) 69.4190i 0.564382i
\(124\) −216.092 97.4136i −1.74268 0.785593i
\(125\) 11.1803 0.0894427
\(126\) −1.94243 3.00631i −0.0154161 0.0238596i
\(127\) 139.469i 1.09818i −0.835763 0.549091i \(-0.814974\pi\)
0.835763 0.549091i \(-0.185026\pi\)
\(128\) −82.1569 + 98.1542i −0.641851 + 0.766829i
\(129\) −62.5543 −0.484917
\(130\) −88.3166 + 57.0628i −0.679359 + 0.438944i
\(131\) 63.4856i 0.484623i 0.970198 + 0.242312i \(0.0779056\pi\)
−0.970198 + 0.242312i \(0.922094\pi\)
\(132\) −26.4217 + 58.6110i −0.200164 + 0.444023i
\(133\) 4.20415 0.0316101
\(134\) 75.6925 + 117.150i 0.564870 + 0.874254i
\(135\) 11.6190i 0.0860663i
\(136\) −4.75901 31.4622i −0.0349927 0.231340i
\(137\) −138.157 −1.00845 −0.504223 0.863573i \(-0.668221\pi\)
−0.504223 + 0.863573i \(0.668221\pi\)
\(138\) −93.3382 + 60.3073i −0.676363 + 0.437009i
\(139\) 29.9578i 0.215523i −0.994177 0.107762i \(-0.965632\pi\)
0.994177 0.107762i \(-0.0343684\pi\)
\(140\) 4.86421 + 2.19277i 0.0347443 + 0.0156626i
\(141\) 128.194 0.909180
\(142\) −64.2733 99.4765i −0.452629 0.700539i
\(143\) 218.180i 1.52573i
\(144\) 31.7860 + 35.9673i 0.220736 + 0.249773i
\(145\) 79.7682 0.550126
\(146\) −139.432 + 90.0891i −0.955012 + 0.617048i
\(147\) 84.2541i 0.573157i
\(148\) −8.85655 + 19.6464i −0.0598416 + 0.132746i
\(149\) −47.3823 −0.318002 −0.159001 0.987278i \(-0.550827\pi\)
−0.159001 + 0.987278i \(0.550827\pi\)
\(150\) 9.39972 + 14.5480i 0.0626648 + 0.0969869i
\(151\) 109.604i 0.725852i 0.931818 + 0.362926i \(0.118222\pi\)
−0.931818 + 0.362926i \(0.881778\pi\)
\(152\) −55.7463 + 8.43227i −0.366752 + 0.0554755i
\(153\) −11.9325 −0.0779904
\(154\) −9.29915 + 6.00833i −0.0603841 + 0.0390151i
\(155\) 132.506i 0.854877i
\(156\) −148.502 66.9442i −0.951936 0.429130i
\(157\) −177.588 −1.13113 −0.565566 0.824703i \(-0.691342\pi\)
−0.565566 + 0.824703i \(0.691342\pi\)
\(158\) 71.4950 + 110.653i 0.452500 + 0.700338i
\(159\) 4.41886i 0.0277916i
\(160\) −68.8967 19.3196i −0.430604 0.120748i
\(161\) −19.1366 −0.118861
\(162\) 15.1188 9.76847i 0.0933257 0.0602992i
\(163\) 96.8778i 0.594342i −0.954824 0.297171i \(-0.903957\pi\)
0.954824 0.297171i \(-0.0960432\pi\)
\(164\) 65.8850 146.152i 0.401738 0.891173i
\(165\) −35.9398 −0.217817
\(166\) 141.002 + 218.230i 0.849408 + 1.31464i
\(167\) 152.605i 0.913801i 0.889518 + 0.456901i \(0.151040\pi\)
−0.889518 + 0.456901i \(0.848960\pi\)
\(168\) 1.23625 + 8.17292i 0.00735862 + 0.0486484i
\(169\) 383.799 2.27100
\(170\) 14.9407 9.65340i 0.0878862 0.0567847i
\(171\) 21.1427i 0.123641i
\(172\) 131.700 + 59.3698i 0.765695 + 0.345173i
\(173\) 155.773 0.900422 0.450211 0.892922i \(-0.351349\pi\)
0.450211 + 0.892922i \(0.351349\pi\)
\(174\) 67.0640 + 103.796i 0.385425 + 0.596527i
\(175\) 2.98270i 0.0170440i
\(176\) 111.254 98.3209i 0.632127 0.558641i
\(177\) −63.0512 −0.356221
\(178\) −219.165 + 141.606i −1.23126 + 0.795540i
\(179\) 126.001i 0.703915i −0.936016 0.351957i \(-0.885516\pi\)
0.936016 0.351957i \(-0.114484\pi\)
\(180\) −11.0275 + 24.4621i −0.0612636 + 0.135901i
\(181\) −346.725 −1.91561 −0.957803 0.287424i \(-0.907201\pi\)
−0.957803 + 0.287424i \(0.907201\pi\)
\(182\) −15.2232 23.5612i −0.0836442 0.129457i
\(183\) 15.1247i 0.0826485i
\(184\) 253.748 38.3823i 1.37906 0.208599i
\(185\) −12.0471 −0.0651192
\(186\) 172.419 111.403i 0.926983 0.598939i
\(187\) 36.9098i 0.197379i
\(188\) −269.896 121.668i −1.43562 0.647171i
\(189\) 3.09971 0.0164006
\(190\) −17.1044 26.4727i −0.0900232 0.139330i
\(191\) 133.159i 0.697167i 0.937278 + 0.348584i \(0.113337\pi\)
−0.937278 + 0.348584i \(0.886663\pi\)
\(192\) −32.7849 105.892i −0.170755 0.551522i
\(193\) −136.246 −0.705940 −0.352970 0.935635i \(-0.614828\pi\)
−0.352970 + 0.935635i \(0.614828\pi\)
\(194\) 156.414 101.062i 0.806259 0.520937i
\(195\) 91.0604i 0.466976i
\(196\) 79.9649 177.386i 0.407984 0.905029i
\(197\) 74.8945 0.380175 0.190087 0.981767i \(-0.439123\pi\)
0.190087 + 0.981767i \(0.439123\pi\)
\(198\) −30.2159 46.7655i −0.152606 0.236189i
\(199\) 251.605i 1.26434i 0.774828 + 0.632172i \(0.217836\pi\)
−0.774828 + 0.632172i \(0.782164\pi\)
\(200\) −5.98240 39.5501i −0.0299120 0.197751i
\(201\) −120.790 −0.600943
\(202\) −6.14966 + 3.97339i −0.0304439 + 0.0196703i
\(203\) 21.2806i 0.104831i
\(204\) 25.1223 + 11.3251i 0.123149 + 0.0555150i
\(205\) 89.6196 0.437169
\(206\) −164.346 254.359i −0.797794 1.23475i
\(207\) 96.2379i 0.464917i
\(208\) 249.114 + 281.884i 1.19767 + 1.35521i
\(209\) 65.3987 0.312913
\(210\) −3.88113 + 2.50766i −0.0184816 + 0.0119412i
\(211\) 228.203i 1.08153i 0.841173 + 0.540766i \(0.181865\pi\)
−0.841173 + 0.540766i \(0.818135\pi\)
\(212\) −4.19390 + 9.30331i −0.0197826 + 0.0438835i
\(213\) 102.567 0.481535
\(214\) −89.8799 139.108i −0.420000 0.650038i
\(215\) 80.7573i 0.375615i
\(216\) −41.1017 + 6.21710i −0.190286 + 0.0287829i
\(217\) 35.3500 0.162903
\(218\) −12.3778 + 7.99751i −0.0567790 + 0.0366858i
\(219\) 143.763i 0.656454i
\(220\) 75.6664 + 34.1102i 0.343938 + 0.155046i
\(221\) −93.5179 −0.423158
\(222\) −10.1284 15.6758i −0.0456234 0.0706118i
\(223\) 85.9549i 0.385448i −0.981253 0.192724i \(-0.938268\pi\)
0.981253 0.192724i \(-0.0617322\pi\)
\(224\) 5.15410 18.3803i 0.0230094 0.0820549i
\(225\) −15.0000 −0.0666667
\(226\) 109.253 70.5902i 0.483421 0.312346i
\(227\) 282.357i 1.24386i 0.783071 + 0.621932i \(0.213652\pi\)
−0.783071 + 0.621932i \(0.786348\pi\)
\(228\) 20.0663 44.5130i 0.0880103 0.195233i
\(229\) 138.263 0.603768 0.301884 0.953345i \(-0.402385\pi\)
0.301884 + 0.953345i \(0.402385\pi\)
\(230\) 77.8563 + 120.499i 0.338506 + 0.523909i
\(231\) 9.58805i 0.0415067i
\(232\) −42.6826 282.178i −0.183977 1.21628i
\(233\) −0.522939 −0.00224438 −0.00112219 0.999999i \(-0.500357\pi\)
−0.00112219 + 0.999999i \(0.500357\pi\)
\(234\) 118.489 76.5577i 0.506364 0.327170i
\(235\) 165.498i 0.704248i
\(236\) 132.746 + 59.8413i 0.562482 + 0.253565i
\(237\) −114.091 −0.481397
\(238\) 2.57534 + 3.98588i 0.0108208 + 0.0167474i
\(239\) 73.6928i 0.308338i 0.988044 + 0.154169i \(0.0492700\pi\)
−0.988044 + 0.154169i \(0.950730\pi\)
\(240\) 46.4336 41.0356i 0.193473 0.170982i
\(241\) 31.3705 0.130168 0.0650840 0.997880i \(-0.479268\pi\)
0.0650840 + 0.997880i \(0.479268\pi\)
\(242\) 58.6080 37.8675i 0.242182 0.156477i
\(243\) 15.5885i 0.0641500i
\(244\) −14.3547 + 31.8429i −0.0588307 + 0.130504i
\(245\) 108.772 0.443966
\(246\) 75.3464 + 116.614i 0.306286 + 0.474042i
\(247\) 165.700i 0.670850i
\(248\) −468.736 + 70.9016i −1.89006 + 0.285894i
\(249\) −225.010 −0.903653
\(250\) 18.7814 12.1350i 0.0751257 0.0485399i
\(251\) 78.7478i 0.313736i 0.987620 + 0.156868i \(0.0501398\pi\)
−0.987620 + 0.156868i \(0.949860\pi\)
\(252\) −6.52602 2.94191i −0.0258969 0.0116742i
\(253\) −297.684 −1.17662
\(254\) −151.378 234.289i −0.595975 0.922397i
\(255\) 15.4048i 0.0604111i
\(256\) −31.4772 + 254.057i −0.122958 + 0.992412i
\(257\) 243.954 0.949236 0.474618 0.880192i \(-0.342586\pi\)
0.474618 + 0.880192i \(0.342586\pi\)
\(258\) −105.083 + 67.8956i −0.407297 + 0.263161i
\(259\) 3.21392i 0.0124090i
\(260\) −86.4246 + 191.715i −0.332402 + 0.737366i
\(261\) −107.020 −0.410039
\(262\) 68.9064 + 106.647i 0.263002 + 0.407050i
\(263\) 102.737i 0.390635i 0.980740 + 0.195317i \(0.0625737\pi\)
−0.980740 + 0.195317i \(0.937426\pi\)
\(264\) 19.2308 + 127.136i 0.0728439 + 0.481576i
\(265\) −5.70472 −0.0215273
\(266\) 7.06239 4.56312i 0.0265503 0.0171546i
\(267\) 225.974i 0.846344i
\(268\) 254.306 + 114.640i 0.948903 + 0.427763i
\(269\) −123.646 −0.459651 −0.229825 0.973232i \(-0.573816\pi\)
−0.229825 + 0.973232i \(0.573816\pi\)
\(270\) −12.6110 19.5182i −0.0467076 0.0722898i
\(271\) 332.371i 1.22646i −0.789904 0.613230i \(-0.789870\pi\)
0.789904 0.613230i \(-0.210130\pi\)
\(272\) −42.1431 47.6868i −0.154938 0.175319i
\(273\) 24.2931 0.0889858
\(274\) −232.085 + 149.954i −0.847026 + 0.547277i
\(275\) 46.3981i 0.168720i
\(276\) −91.3386 + 202.616i −0.330937 + 0.734115i
\(277\) −125.916 −0.454571 −0.227286 0.973828i \(-0.572985\pi\)
−0.227286 + 0.973828i \(0.572985\pi\)
\(278\) −32.5157 50.3249i −0.116963 0.181025i
\(279\) 177.775i 0.637188i
\(280\) 10.5512 1.59599i 0.0376829 0.00569996i
\(281\) 52.5628 0.187056 0.0935281 0.995617i \(-0.470186\pi\)
0.0935281 + 0.995617i \(0.470186\pi\)
\(282\) 215.349 139.140i 0.763649 0.493405i
\(283\) 199.288i 0.704199i −0.935963 0.352100i \(-0.885468\pi\)
0.935963 0.352100i \(-0.114532\pi\)
\(284\) −215.941 97.3454i −0.760355 0.342766i
\(285\) 27.2951 0.0957722
\(286\) −236.809 366.512i −0.828004 1.28151i
\(287\) 23.9088i 0.0833058i
\(288\) 92.4346 + 25.9200i 0.320953 + 0.0900001i
\(289\) −273.179 −0.945258
\(290\) 134.000 86.5793i 0.462068 0.298549i
\(291\) 161.274i 0.554205i
\(292\) −136.445 + 302.674i −0.467276 + 1.03656i
\(293\) 102.161 0.348672 0.174336 0.984686i \(-0.444222\pi\)
0.174336 + 0.984686i \(0.444222\pi\)
\(294\) 91.4482 + 141.535i 0.311048 + 0.481413i
\(295\) 81.3987i 0.275928i
\(296\) 6.44617 + 42.6161i 0.0217776 + 0.143973i
\(297\) 48.2184 0.162351
\(298\) −79.5957 + 51.4281i −0.267100 + 0.172577i
\(299\) 754.238i 2.52254i
\(300\) 31.5805 + 14.2364i 0.105268 + 0.0474546i
\(301\) −21.5445 −0.0715763
\(302\) 118.962 + 184.119i 0.393915 + 0.609666i
\(303\) 6.34071i 0.0209264i
\(304\) −84.4939 + 74.6713i −0.277941 + 0.245629i
\(305\) −19.5259 −0.0640192
\(306\) −20.0450 + 12.9514i −0.0655065 + 0.0423248i
\(307\) 328.391i 1.06968i −0.844954 0.534839i \(-0.820372\pi\)
0.844954 0.534839i \(-0.179628\pi\)
\(308\) −9.09994 + 20.1863i −0.0295453 + 0.0655401i
\(309\) 262.262 0.848743
\(310\) −143.820 222.592i −0.463936 0.718038i
\(311\) 95.4377i 0.306874i −0.988158 0.153437i \(-0.950966\pi\)
0.988158 0.153437i \(-0.0490342\pi\)
\(312\) −322.123 + 48.7248i −1.03245 + 0.156169i
\(313\) 550.408 1.75849 0.879246 0.476368i \(-0.158047\pi\)
0.879246 + 0.476368i \(0.158047\pi\)
\(314\) −298.323 + 192.751i −0.950073 + 0.613858i
\(315\) 4.00171i 0.0127038i
\(316\) 240.203 + 108.283i 0.760137 + 0.342668i
\(317\) 439.394 1.38610 0.693051 0.720889i \(-0.256266\pi\)
0.693051 + 0.720889i \(0.256266\pi\)
\(318\) −4.79617 7.42307i −0.0150823 0.0233430i
\(319\) 331.036i 1.03773i
\(320\) −136.706 + 42.3251i −0.427207 + 0.132266i
\(321\) 143.430 0.446822
\(322\) −32.1468 + 20.7706i −0.0998348 + 0.0645048i
\(323\) 28.0317i 0.0867855i
\(324\) 14.7949 32.8194i 0.0456632 0.101294i
\(325\) −117.558 −0.361718
\(326\) −105.150 162.741i −0.322545 0.499206i
\(327\) 12.7624i 0.0390286i
\(328\) −47.9539 317.026i −0.146201 0.966544i
\(329\) 44.1517 0.134200
\(330\) −60.3740 + 39.0086i −0.182951 + 0.118208i
\(331\) 479.922i 1.44992i −0.688794 0.724958i \(-0.741859\pi\)
0.688794 0.724958i \(-0.258141\pi\)
\(332\) 473.727 + 213.555i 1.42689 + 0.643237i
\(333\) 16.1628 0.0485370
\(334\) 165.635 + 256.355i 0.495913 + 0.767530i
\(335\) 155.939i 0.465489i
\(336\) 10.9475 + 12.3876i 0.0325819 + 0.0368678i
\(337\) 58.8437 0.174610 0.0873052 0.996182i \(-0.472174\pi\)
0.0873052 + 0.996182i \(0.472174\pi\)
\(338\) 644.730 416.570i 1.90748 1.23246i
\(339\) 112.647i 0.332293i
\(340\) 14.6206 32.4328i 0.0430017 0.0953905i
\(341\) 549.897 1.61260
\(342\) 22.9480 + 35.5168i 0.0670993 + 0.103850i
\(343\) 58.2486i 0.169821i
\(344\) 285.676 43.2118i 0.830454 0.125616i
\(345\) −124.243 −0.360123
\(346\) 261.677 169.074i 0.756293 0.488653i
\(347\) 12.1484i 0.0350099i 0.999847 + 0.0175049i \(0.00557228\pi\)
−0.999847 + 0.0175049i \(0.994428\pi\)
\(348\) 225.317 + 101.572i 0.647462 + 0.291874i
\(349\) −30.9277 −0.0886180 −0.0443090 0.999018i \(-0.514109\pi\)
−0.0443090 + 0.999018i \(0.514109\pi\)
\(350\) 3.23738 + 5.01052i 0.00924965 + 0.0143158i
\(351\) 122.170i 0.348063i
\(352\) 80.1760 285.919i 0.227773 0.812271i
\(353\) −288.065 −0.816048 −0.408024 0.912971i \(-0.633782\pi\)
−0.408024 + 0.912971i \(0.633782\pi\)
\(354\) −105.917 + 68.4348i −0.299201 + 0.193319i
\(355\) 132.413i 0.372995i
\(356\) −214.470 + 475.757i −0.602444 + 1.33640i
\(357\) −4.10971 −0.0115118
\(358\) −136.759 211.664i −0.382010 0.591240i
\(359\) 663.911i 1.84933i 0.380776 + 0.924667i \(0.375657\pi\)
−0.380776 + 0.924667i \(0.624343\pi\)
\(360\) 8.02624 + 53.0620i 0.0222951 + 0.147395i
\(361\) 311.332 0.862415
\(362\) −582.450 + 376.330i −1.60898 + 1.03959i
\(363\) 60.4287i 0.166470i
\(364\) −51.1459 23.0564i −0.140511 0.0633418i
\(365\) −185.598 −0.508487
\(366\) −16.4161 25.4074i −0.0448527 0.0694190i
\(367\) 6.08529i 0.0165812i 0.999966 + 0.00829059i \(0.00263901\pi\)
−0.999966 + 0.00829059i \(0.997361\pi\)
\(368\) 384.602 339.891i 1.04511 0.923618i
\(369\) −120.237 −0.325846
\(370\) −20.2374 + 13.0757i −0.0546957 + 0.0353397i
\(371\) 1.52191i 0.00410218i
\(372\) 168.725 374.282i 0.453562 1.00613i
\(373\) −204.741 −0.548903 −0.274451 0.961601i \(-0.588496\pi\)
−0.274451 + 0.961601i \(0.588496\pi\)
\(374\) 40.0614 + 62.0034i 0.107116 + 0.165784i
\(375\) 19.3649i 0.0516398i
\(376\) −585.445 + 88.5552i −1.55703 + 0.235519i
\(377\) −838.742 −2.22478
\(378\) 5.20709 3.36438i 0.0137754 0.00890048i
\(379\) 402.331i 1.06156i −0.847510 0.530780i \(-0.821899\pi\)
0.847510 0.530780i \(-0.178101\pi\)
\(380\) −57.4661 25.9055i −0.151227 0.0681725i
\(381\) 241.568 0.634036
\(382\) 144.529 + 223.689i 0.378348 + 0.585573i
\(383\) 331.751i 0.866191i −0.901348 0.433096i \(-0.857421\pi\)
0.901348 0.433096i \(-0.142579\pi\)
\(384\) −170.008 142.300i −0.442729 0.370573i
\(385\) −12.3781 −0.0321510
\(386\) −228.875 + 147.880i −0.592941 + 0.383109i
\(387\) 108.347i 0.279967i
\(388\) 153.063 339.540i 0.394493 0.875102i
\(389\) −623.310 −1.60234 −0.801169 0.598438i \(-0.795788\pi\)
−0.801169 + 0.598438i \(0.795788\pi\)
\(390\) −98.8356 152.969i −0.253425 0.392228i
\(391\) 127.596i 0.326332i
\(392\) −58.2018 384.776i −0.148474 0.981572i
\(393\) −109.960 −0.279797
\(394\) 125.812 81.2894i 0.319321 0.206318i
\(395\) 147.291i 0.372889i
\(396\) −101.517 45.7636i −0.256357 0.115565i
\(397\) −355.449 −0.895338 −0.447669 0.894199i \(-0.647746\pi\)
−0.447669 + 0.894199i \(0.647746\pi\)
\(398\) 273.088 + 422.661i 0.686151 + 1.06196i
\(399\) 7.28180i 0.0182501i
\(400\) −52.9767 59.9455i −0.132442 0.149864i
\(401\) −542.927 −1.35393 −0.676966 0.736014i \(-0.736706\pi\)
−0.676966 + 0.736014i \(0.736706\pi\)
\(402\) −202.910 + 131.103i −0.504751 + 0.326128i
\(403\) 1393.27i 3.45724i
\(404\) −6.01792 + 13.3495i −0.0148958 + 0.0330433i
\(405\) 20.1246 0.0496904
\(406\) 23.0977 + 35.7485i 0.0568908 + 0.0880505i
\(407\) 49.9950i 0.122838i
\(408\) 54.4941 8.24285i 0.133564 0.0202031i
\(409\) −108.497 −0.265273 −0.132636 0.991165i \(-0.542344\pi\)
−0.132636 + 0.991165i \(0.542344\pi\)
\(410\) 150.549 97.2718i 0.367192 0.237248i
\(411\) 239.295i 0.582227i
\(412\) −552.156 248.910i −1.34018 0.604151i
\(413\) −21.7156 −0.0525801
\(414\) −104.455 161.666i −0.252307 0.390499i
\(415\) 290.486i 0.699966i
\(416\) 724.431 + 203.141i 1.74142 + 0.488320i
\(417\) 51.8884 0.124433
\(418\) 109.861 70.9828i 0.262825 0.169815i
\(419\) 172.176i 0.410921i −0.978665 0.205460i \(-0.934131\pi\)
0.978665 0.205460i \(-0.0658691\pi\)
\(420\) −3.79799 + 8.42505i −0.00904283 + 0.0200597i
\(421\) 478.522 1.13663 0.568316 0.822810i \(-0.307595\pi\)
0.568316 + 0.822810i \(0.307595\pi\)
\(422\) 247.688 + 383.350i 0.586940 + 0.908412i
\(423\) 222.039i 0.524915i
\(424\) 3.05250 + 20.1803i 0.00719929 + 0.0475950i
\(425\) 19.8875 0.0467942
\(426\) 172.298 111.325i 0.404456 0.261326i
\(427\) 5.20912i 0.0121993i
\(428\) −301.972 136.128i −0.705541 0.318056i
\(429\) 377.898 0.880882
\(430\) 87.6528 + 135.661i 0.203844 + 0.315491i
\(431\) 290.722i 0.674530i −0.941410 0.337265i \(-0.890498\pi\)
0.941410 0.337265i \(-0.109502\pi\)
\(432\) −62.2972 + 55.0550i −0.144207 + 0.127442i
\(433\) 53.7726 0.124186 0.0620931 0.998070i \(-0.480222\pi\)
0.0620931 + 0.998070i \(0.480222\pi\)
\(434\) 59.3832 38.3684i 0.136828 0.0884065i
\(435\) 138.163i 0.317615i
\(436\) −12.1127 + 26.8694i −0.0277813 + 0.0616271i
\(437\) 226.081 0.517347
\(438\) −156.039 241.503i −0.356253 0.551376i
\(439\) 328.657i 0.748650i 0.927298 + 0.374325i \(0.122126\pi\)
−0.927298 + 0.374325i \(0.877874\pi\)
\(440\) 164.132 24.8268i 0.373027 0.0564246i
\(441\) −145.932 −0.330913
\(442\) −157.097 + 101.503i −0.355424 + 0.229645i
\(443\) 428.910i 0.968194i 0.875014 + 0.484097i \(0.160852\pi\)
−0.875014 + 0.484097i \(0.839148\pi\)
\(444\) −34.0286 15.3400i −0.0766410 0.0345496i
\(445\) −291.731 −0.655575
\(446\) −93.2942 144.392i −0.209180 0.323750i
\(447\) 82.0685i 0.183599i
\(448\) −11.2915 36.4706i −0.0252043 0.0814075i
\(449\) 409.229 0.911423 0.455711 0.890128i \(-0.349385\pi\)
0.455711 + 0.890128i \(0.349385\pi\)
\(450\) −25.1979 + 16.2808i −0.0559954 + 0.0361795i
\(451\) 371.919i 0.824654i
\(452\) 106.913 237.164i 0.236533 0.524698i
\(453\) −189.839 −0.419071
\(454\) 306.466 + 474.321i 0.675036 + 1.04476i
\(455\) 31.3623i 0.0689281i
\(456\) −14.6051 96.5555i −0.0320288 0.211745i
\(457\) 768.561 1.68175 0.840876 0.541228i \(-0.182040\pi\)
0.840876 + 0.541228i \(0.182040\pi\)
\(458\) 232.262 150.068i 0.507123 0.327660i
\(459\) 20.6677i 0.0450278i
\(460\) 261.576 + 117.918i 0.568643 + 0.256343i
\(461\) −316.563 −0.686687 −0.343343 0.939210i \(-0.611559\pi\)
−0.343343 + 0.939210i \(0.611559\pi\)
\(462\) −10.4067 16.1066i −0.0225254 0.0348628i
\(463\) 491.208i 1.06093i −0.847708 0.530463i \(-0.822018\pi\)
0.847708 0.530463i \(-0.177982\pi\)
\(464\) −377.972 427.692i −0.814596 0.921751i
\(465\) 229.507 0.493564
\(466\) −0.878466 + 0.567591i −0.00188512 + 0.00121801i
\(467\) 410.393i 0.878785i −0.898295 0.439393i \(-0.855194\pi\)
0.898295 0.439393i \(-0.144806\pi\)
\(468\) 115.951 257.213i 0.247758 0.549600i
\(469\) −41.6014 −0.0887024
\(470\) −179.629 278.014i −0.382190 0.591520i
\(471\) 307.591i 0.653060i
\(472\) 287.945 43.5550i 0.610054 0.0922776i
\(473\) −335.141 −0.708542
\(474\) −191.657 + 123.833i −0.404341 + 0.261251i
\(475\) 35.2378i 0.0741848i
\(476\) 8.65243 + 3.90049i 0.0181774 + 0.00819431i
\(477\) 7.65369 0.0160455
\(478\) 79.9851 + 123.794i 0.167333 + 0.258983i
\(479\) 198.918i 0.415277i −0.978206 0.207638i \(-0.933422\pi\)
0.978206 0.207638i \(-0.0665778\pi\)
\(480\) 33.4626 119.333i 0.0697137 0.248609i
\(481\) 126.672 0.263351
\(482\) 52.6981 34.0491i 0.109332 0.0706413i
\(483\) 33.1455i 0.0686242i
\(484\) 57.3524 127.224i 0.118497 0.262860i
\(485\) 208.203 0.429285
\(486\) 16.9195 + 26.1865i 0.0348138 + 0.0538816i
\(487\) 204.762i 0.420456i 0.977652 + 0.210228i \(0.0674206\pi\)
−0.977652 + 0.210228i \(0.932579\pi\)
\(488\) 10.4479 + 69.0721i 0.0214097 + 0.141541i
\(489\) 167.797 0.343144
\(490\) 182.721 118.059i 0.372901 0.240937i
\(491\) 788.598i 1.60611i −0.595908 0.803053i \(-0.703208\pi\)
0.595908 0.803053i \(-0.296792\pi\)
\(492\) 253.143 + 114.116i 0.514519 + 0.231944i
\(493\) 141.891 0.287812
\(494\) 179.848 + 278.353i 0.364066 + 0.563468i
\(495\) 62.2496i 0.125757i
\(496\) −710.456 + 627.864i −1.43237 + 1.26586i
\(497\) 35.3253 0.0710771
\(498\) −377.985 + 244.222i −0.759006 + 0.490406i
\(499\) 740.385i 1.48374i −0.670545 0.741869i \(-0.733940\pi\)
0.670545 0.741869i \(-0.266060\pi\)
\(500\) 18.3791 40.7702i 0.0367582 0.0815404i
\(501\) −264.319 −0.527583
\(502\) 85.4717 + 132.285i 0.170262 + 0.263517i
\(503\) 70.8800i 0.140914i −0.997515 0.0704572i \(-0.977554\pi\)
0.997515 0.0704572i \(-0.0224458\pi\)
\(504\) −14.1559 + 2.14124i −0.0280871 + 0.00424850i
\(505\) −8.18582 −0.0162095
\(506\) −500.068 + 323.102i −0.988277 + 0.638541i
\(507\) 664.760i 1.31116i
\(508\) −508.588 229.270i −1.00116 0.451318i
\(509\) 522.642 1.02680 0.513400 0.858149i \(-0.328386\pi\)
0.513400 + 0.858149i \(0.328386\pi\)
\(510\) 16.7202 + 25.8780i 0.0327847 + 0.0507411i
\(511\) 49.5139i 0.0968961i
\(512\) 222.873 + 460.946i 0.435299 + 0.900286i
\(513\) −36.6202 −0.0713844
\(514\) 409.809 264.784i 0.797293 0.515144i
\(515\) 338.578i 0.657433i
\(516\) −102.831 + 228.110i −0.199286 + 0.442074i
\(517\) 686.813 1.32846
\(518\) −3.48834 5.39894i −0.00673425 0.0104227i
\(519\) 269.807i 0.519859i
\(520\) 62.9034 + 415.859i 0.120968 + 0.799729i
\(521\) 304.082 0.583650 0.291825 0.956472i \(-0.405738\pi\)
0.291825 + 0.956472i \(0.405738\pi\)
\(522\) −179.779 + 116.158i −0.344405 + 0.222525i
\(523\) 174.416i 0.333491i 0.986000 + 0.166746i \(0.0533259\pi\)
−0.986000 + 0.166746i \(0.946674\pi\)
\(524\) 231.507 + 104.362i 0.441806 + 0.199165i
\(525\) −5.16618 −0.00984035
\(526\) 111.509 + 172.584i 0.211995 + 0.328106i
\(527\) 235.701i 0.447251i
\(528\) 170.297 + 192.698i 0.322532 + 0.364959i
\(529\) −500.081 −0.945333
\(530\) −9.58315 + 6.19182i −0.0180814 + 0.0116827i
\(531\) 109.208i 0.205664i
\(532\) 6.91109 15.3308i 0.0129908 0.0288174i
\(533\) −942.327 −1.76797
\(534\) −245.269 379.605i −0.459305 0.710871i
\(535\) 185.167i 0.346106i
\(536\) 551.628 83.4401i 1.02916 0.155672i
\(537\) 218.240 0.406405
\(538\) −207.708 + 134.204i −0.386075 + 0.249449i
\(539\) 451.399i 0.837476i
\(540\) −42.3696 19.1001i −0.0784623 0.0353706i
\(541\) −262.199 −0.484655 −0.242328 0.970194i \(-0.577911\pi\)
−0.242328 + 0.970194i \(0.577911\pi\)
\(542\) −360.750 558.337i −0.665591 1.03014i
\(543\) 600.545i 1.10598i
\(544\) −122.553 34.3657i −0.225281 0.0631722i
\(545\) −16.4761 −0.0302314
\(546\) 40.8091 26.3674i 0.0747420 0.0482920i
\(547\) 146.179i 0.267237i −0.991033 0.133619i \(-0.957340\pi\)
0.991033 0.133619i \(-0.0426598\pi\)
\(548\) −227.113 + 503.804i −0.414440 + 0.919350i
\(549\) 26.1967 0.0477171
\(550\) 50.3599 + 77.9425i 0.0915634 + 0.141714i
\(551\) 251.411i 0.456281i
\(552\) 66.4800 + 439.504i 0.120435 + 0.796203i
\(553\) −39.2944 −0.0710568
\(554\) −211.522 + 136.668i −0.381809 + 0.246693i
\(555\) 20.8661i 0.0375966i
\(556\) −109.244 49.2468i −0.196482 0.0885734i
\(557\) 187.700 0.336984 0.168492 0.985703i \(-0.446110\pi\)
0.168492 + 0.985703i \(0.446110\pi\)
\(558\) 192.955 + 298.638i 0.345797 + 0.535194i
\(559\) 849.142i 1.51904i
\(560\) 15.9923 14.1332i 0.0285577 0.0252378i
\(561\) −63.9296 −0.113957
\(562\) 88.2982 57.0509i 0.157114 0.101514i
\(563\) 447.848i 0.795467i 0.917501 + 0.397734i \(0.130203\pi\)
−0.917501 + 0.397734i \(0.869797\pi\)
\(564\) 210.736 467.473i 0.373645 0.828853i
\(565\) 145.427 0.257393
\(566\) −216.305 334.777i −0.382164 0.591479i
\(567\) 5.36886i 0.00946888i
\(568\) −468.408 + 70.8520i −0.824662 + 0.124740i
\(569\) 1078.91 1.89615 0.948077 0.318042i \(-0.103025\pi\)
0.948077 + 0.318042i \(0.103025\pi\)
\(570\) 45.8520 29.6257i 0.0804421 0.0519749i
\(571\) 936.324i 1.63980i 0.572509 + 0.819899i \(0.305970\pi\)
−0.572509 + 0.819899i \(0.694030\pi\)
\(572\) −795.613 358.660i −1.39093 0.627028i
\(573\) −230.638 −0.402510
\(574\) 25.9502 + 40.1634i 0.0452095 + 0.0699711i
\(575\) 160.396i 0.278950i
\(576\) 183.411 56.7851i 0.318421 0.0985853i
\(577\) −544.832 −0.944250 −0.472125 0.881532i \(-0.656513\pi\)
−0.472125 + 0.881532i \(0.656513\pi\)
\(578\) −458.904 + 296.505i −0.793951 + 0.512985i
\(579\) 235.986i 0.407575i
\(580\) 131.129 290.883i 0.226084 0.501522i
\(581\) −77.4960 −0.133384
\(582\) 175.044 + 270.917i 0.300763 + 0.465494i
\(583\) 23.6745i 0.0406080i
\(584\) 99.3101 + 656.547i 0.170052 + 1.12422i
\(585\) 157.721 0.269609
\(586\) 171.616 110.884i 0.292861 0.189222i
\(587\) 337.889i 0.575619i 0.957688 + 0.287810i \(0.0929271\pi\)
−0.957688 + 0.287810i \(0.907073\pi\)
\(588\) 307.241 + 138.503i 0.522519 + 0.235550i
\(589\) −417.628 −0.709045
\(590\) 88.3490 + 136.739i 0.149744 + 0.231760i
\(591\) 129.721i 0.219494i
\(592\) 57.0836 + 64.5926i 0.0964249 + 0.109109i
\(593\) 567.269 0.956608 0.478304 0.878194i \(-0.341252\pi\)
0.478304 + 0.878194i \(0.341252\pi\)
\(594\) 81.0002 52.3355i 0.136364 0.0881069i
\(595\) 5.30561i 0.00891699i
\(596\) −77.8906 + 172.784i −0.130689 + 0.289906i
\(597\) −435.792 −0.729969
\(598\) −818.640 1267.02i −1.36896 2.11876i
\(599\) 762.966i 1.27373i 0.770974 + 0.636867i \(0.219770\pi\)
−0.770974 + 0.636867i \(0.780230\pi\)
\(600\) 68.5028 10.3618i 0.114171 0.0172697i
\(601\) −790.102 −1.31464 −0.657322 0.753609i \(-0.728311\pi\)
−0.657322 + 0.753609i \(0.728311\pi\)
\(602\) −36.1917 + 23.3841i −0.0601192 + 0.0388440i
\(603\) 209.214i 0.346955i
\(604\) 399.680 + 180.175i 0.661722 + 0.298302i
\(605\) 78.0132 0.128947
\(606\) −6.88212 10.6515i −0.0113566 0.0175768i
\(607\) 522.994i 0.861605i −0.902446 0.430802i \(-0.858231\pi\)
0.902446 0.430802i \(-0.141769\pi\)
\(608\) −60.8909 + 217.146i −0.100150 + 0.357148i
\(609\) −36.8591 −0.0605240
\(610\) −32.8008 + 21.1931i −0.0537717 + 0.0347428i
\(611\) 1740.17i 2.84807i
\(612\) −19.6156 + 43.5131i −0.0320516 + 0.0710999i
\(613\) 1026.91 1.67522 0.837609 0.546270i \(-0.183953\pi\)
0.837609 + 0.546270i \(0.183953\pi\)
\(614\) −356.431 551.652i −0.580506 0.898455i
\(615\) 155.226i 0.252399i
\(616\) 6.62332 + 43.7872i 0.0107521 + 0.0710831i
\(617\) −479.223 −0.776698 −0.388349 0.921512i \(-0.626954\pi\)
−0.388349 + 0.921512i \(0.626954\pi\)
\(618\) 440.563 284.655i 0.712886 0.460607i
\(619\) 507.654i 0.820119i −0.912059 0.410059i \(-0.865508\pi\)
0.912059 0.410059i \(-0.134492\pi\)
\(620\) −483.196 217.823i −0.779348 0.351328i
\(621\) 166.689 0.268420
\(622\) −103.587 160.322i −0.166538 0.257753i
\(623\) 77.8282i 0.124925i
\(624\) −488.237 + 431.479i −0.782432 + 0.691473i
\(625\) 25.0000 0.0400000
\(626\) 924.609 597.405i 1.47701 0.954321i
\(627\) 113.274i 0.180660i
\(628\) −291.932 + 647.591i −0.464860 + 1.03120i
\(629\) −21.4293 −0.0340688
\(630\) −4.34340 6.72232i −0.00689428 0.0106703i
\(631\) 460.186i 0.729297i −0.931145 0.364648i \(-0.881189\pi\)
0.931145 0.364648i \(-0.118811\pi\)
\(632\) 521.037 78.8128i 0.824426 0.124704i
\(633\) −395.259 −0.624423
\(634\) 738.122 476.912i 1.16423 0.752228i
\(635\) 311.862i 0.491122i
\(636\) −16.1138 7.26405i −0.0253362 0.0114215i
\(637\) −1143.71 −1.79546
\(638\) 359.302 + 556.095i 0.563169 + 0.871622i
\(639\) 177.651i 0.278014i
\(640\) −183.708 + 219.479i −0.287045 + 0.342937i
\(641\) 250.774 0.391223 0.195612 0.980681i \(-0.437331\pi\)
0.195612 + 0.980681i \(0.437331\pi\)
\(642\) 240.942 155.677i 0.375299 0.242487i
\(643\) 590.355i 0.918126i −0.888404 0.459063i \(-0.848185\pi\)
0.888404 0.459063i \(-0.151815\pi\)
\(644\) −31.4581 + 69.7834i −0.0488480 + 0.108359i
\(645\) −139.876 −0.216862
\(646\) −30.4252 47.0894i −0.0470979 0.0728939i
\(647\) 319.341i 0.493572i −0.969070 0.246786i \(-0.920626\pi\)
0.969070 0.246786i \(-0.0793744\pi\)
\(648\) −10.7683 71.1902i −0.0166178 0.109861i
\(649\) −337.803 −0.520497
\(650\) −197.482 + 127.596i −0.303818 + 0.196302i
\(651\) 61.2280i 0.0940523i
\(652\) −353.274 159.255i −0.541832 0.244256i
\(653\) 88.5949 0.135674 0.0678369 0.997696i \(-0.478390\pi\)
0.0678369 + 0.997696i \(0.478390\pi\)
\(654\) −13.8521 21.4390i −0.0211806 0.0327814i
\(655\) 141.958i 0.216730i
\(656\) −424.652 480.512i −0.647335 0.732488i
\(657\) 249.006 0.379004
\(658\) 74.1688 47.9216i 0.112719 0.0728292i
\(659\) 758.423i 1.15087i 0.817847 + 0.575435i \(0.195167\pi\)
−0.817847 + 0.575435i \(0.804833\pi\)
\(660\) −59.0806 + 131.058i −0.0895161 + 0.198573i
\(661\) 527.327 0.797771 0.398885 0.917001i \(-0.369397\pi\)
0.398885 + 0.917001i \(0.369397\pi\)
\(662\) −520.900 806.203i −0.786859 1.21783i
\(663\) 161.978i 0.244310i
\(664\) 1027.59 155.434i 1.54757 0.234087i
\(665\) 9.40076 0.0141365
\(666\) 27.1513 17.5429i 0.0407677 0.0263407i
\(667\) 1144.38i 1.71571i
\(668\) 556.488 + 250.863i 0.833066 + 0.375544i
\(669\) 148.878 0.222538
\(670\) 169.254 + 261.956i 0.252617 + 0.390978i
\(671\) 81.0318i 0.120763i
\(672\) 31.8356 + 8.92717i 0.0473744 + 0.0132845i
\(673\) 120.657 0.179283 0.0896415 0.995974i \(-0.471428\pi\)
0.0896415 + 0.995974i \(0.471428\pi\)
\(674\) 98.8493 63.8681i 0.146661 0.0947598i
\(675\) 25.9808i 0.0384900i
\(676\) 630.918 1399.56i 0.933311 2.07036i
\(677\) −219.196 −0.323776 −0.161888 0.986809i \(-0.551758\pi\)
−0.161888 + 0.986809i \(0.551758\pi\)
\(678\) 122.266 + 189.232i 0.180333 + 0.279103i
\(679\) 55.5446i 0.0818035i
\(680\) −10.6415 70.3516i −0.0156492 0.103458i
\(681\) −489.057 −0.718145
\(682\) 923.751 596.850i 1.35447 0.875146i
\(683\) 205.502i 0.300881i −0.988619 0.150441i \(-0.951931\pi\)
0.988619 0.150441i \(-0.0480693\pi\)
\(684\) 77.0988 + 34.7559i 0.112718 + 0.0508128i
\(685\) −308.929 −0.450991
\(686\) 63.2222 + 97.8496i 0.0921606 + 0.142638i
\(687\) 239.478i 0.348585i
\(688\) 432.995 382.659i 0.629354 0.556190i
\(689\) 59.9837 0.0870591
\(690\) −208.710 + 134.851i −0.302479 + 0.195436i
\(691\) 109.536i 0.158519i −0.996854 0.0792593i \(-0.974744\pi\)
0.996854 0.0792593i \(-0.0252555\pi\)
\(692\) 256.071 568.042i 0.370045 0.820869i
\(693\) 16.6070 0.0239639
\(694\) 13.1857 + 20.4077i 0.0189996 + 0.0294059i
\(695\) 66.9876i 0.0963850i
\(696\) 488.746 73.9284i 0.702221 0.106219i
\(697\) 159.415 0.228716
\(698\) −51.9543 + 33.5685i −0.0744331 + 0.0480924i
\(699\) 0.905758i 0.00129579i
\(700\) 10.8767 + 4.90318i 0.0155381 + 0.00700455i
\(701\) 168.847 0.240865 0.120433 0.992721i \(-0.461572\pi\)
0.120433 + 0.992721i \(0.461572\pi\)
\(702\) 132.602 + 205.229i 0.188892 + 0.292349i
\(703\) 37.9695i 0.0540106i
\(704\) −175.648 567.327i −0.249500 0.805863i
\(705\) 286.651 0.406598
\(706\) −483.909 + 312.661i −0.685424 + 0.442863i
\(707\) 2.18382i 0.00308885i
\(708\) −103.648 + 229.922i −0.146396 + 0.324749i
\(709\) −554.846 −0.782576 −0.391288 0.920268i \(-0.627970\pi\)
−0.391288 + 0.920268i \(0.627970\pi\)
\(710\) −143.720 222.436i −0.202422 0.313290i
\(711\) 197.612i 0.277935i
\(712\) 156.100 + 1031.99i 0.219242 + 1.44942i
\(713\) 1900.97 2.66616
\(714\) −6.90374 + 4.46062i −0.00966911 + 0.00624737i
\(715\) 487.864i 0.682328i
\(716\) −459.474 207.130i −0.641723 0.289287i
\(717\) −127.640 −0.178019
\(718\) 720.600 + 1115.28i 1.00362 + 1.55331i
\(719\) 377.485i 0.525014i 0.964930 + 0.262507i \(0.0845494\pi\)
−0.964930 + 0.262507i \(0.915451\pi\)
\(720\) 71.0758 + 80.4254i 0.0987163 + 0.111702i
\(721\) 90.3261 0.125279
\(722\) 522.995 337.915i 0.724369 0.468027i
\(723\) 54.3353i 0.0751525i
\(724\) −569.972 + 1264.37i −0.787255 + 1.74636i
\(725\) 178.367 0.246024
\(726\) 65.5885 + 101.512i 0.0903423 + 0.139824i
\(727\) 173.183i 0.238216i 0.992881 + 0.119108i \(0.0380035\pi\)
−0.992881 + 0.119108i \(0.961997\pi\)
\(728\) −110.943 + 16.7814i −0.152394 + 0.0230514i
\(729\) −27.0000 −0.0370370
\(730\) −311.779 + 201.445i −0.427094 + 0.275952i
\(731\) 143.651i 0.196513i
\(732\) −55.1536 24.8631i −0.0753464 0.0339659i
\(733\) 278.722 0.380249 0.190124 0.981760i \(-0.439111\pi\)
0.190124 + 0.981760i \(0.439111\pi\)
\(734\) 6.60489 + 10.2225i 0.00899849 + 0.0139270i
\(735\) 188.398i 0.256324i
\(736\) 277.165 988.412i 0.376583 1.34295i
\(737\) −647.142 −0.878075
\(738\) −201.982 + 130.504i −0.273688 + 0.176834i
\(739\) 521.363i 0.705498i 0.935718 + 0.352749i \(0.114753\pi\)
−0.935718 + 0.352749i \(0.885247\pi\)
\(740\) −19.8039 + 43.9308i −0.0267620 + 0.0593659i
\(741\) −287.001 −0.387315
\(742\) −1.65186 2.55660i −0.00222622 0.00344555i
\(743\) 1277.93i 1.71996i −0.510326 0.859981i \(-0.670475\pi\)
0.510326 0.859981i \(-0.329525\pi\)
\(744\) −122.805 811.874i −0.165061 1.09123i
\(745\) −105.950 −0.142215
\(746\) −343.936 + 222.223i −0.461041 + 0.297886i
\(747\) 389.728i 0.521724i
\(748\) 134.595 + 60.6751i 0.179940 + 0.0811164i
\(749\) 49.3989 0.0659532
\(750\) 21.0184 + 32.5304i 0.0280245 + 0.0433739i
\(751\) 1165.31i 1.55168i 0.630930 + 0.775840i \(0.282673\pi\)
−0.630930 + 0.775840i \(0.717327\pi\)
\(752\) −887.350 + 784.194i −1.17999 + 1.04281i
\(753\) −136.395 −0.181136
\(754\) −1408.97 + 910.359i −1.86866 + 1.20737i
\(755\) 245.081i 0.324611i
\(756\) 5.09554 11.3034i 0.00674013 0.0149516i
\(757\) 1063.75 1.40522 0.702611 0.711574i \(-0.252017\pi\)
0.702611 + 0.711574i \(0.252017\pi\)
\(758\) −436.685 675.861i −0.576101 0.891638i
\(759\) 515.604i 0.679320i
\(760\) −124.653 + 18.8551i −0.164017 + 0.0248094i
\(761\) −677.847 −0.890732 −0.445366 0.895349i \(-0.646926\pi\)
−0.445366 + 0.895349i \(0.646926\pi\)
\(762\) 405.800 262.194i 0.532546 0.344087i
\(763\) 4.39551i 0.00576083i
\(764\) 485.577 + 218.897i 0.635572 + 0.286514i
\(765\) −26.6819 −0.0348784
\(766\) −360.078 557.296i −0.470076 0.727541i
\(767\) 855.887i 1.11589i
\(768\) −440.040 54.5201i −0.572969 0.0709898i
\(769\) −1289.59 −1.67697 −0.838486 0.544922i \(-0.816559\pi\)
−0.838486 + 0.544922i \(0.816559\pi\)
\(770\) −20.7935 + 13.4350i −0.0270046 + 0.0174481i
\(771\) 422.540i 0.548042i
\(772\) −223.972 + 496.836i −0.290119 + 0.643570i
\(773\) −750.339 −0.970684 −0.485342 0.874324i \(-0.661305\pi\)
−0.485342 + 0.874324i \(0.661305\pi\)
\(774\) −117.599 182.008i −0.151936 0.235153i
\(775\) 296.292i 0.382313i
\(776\) −111.406 736.513i −0.143564 0.949114i
\(777\) 5.56667 0.00716432
\(778\) −1047.07 + 676.532i −1.34585 + 0.869578i
\(779\) 282.460i 0.362593i